For various reasons it's actually fairly difficult to do controlled studies like you say. I know a guy doing a study right now who is actually running it backwards. That is, instead of looking at how GPA affects future income, he is looking at how past income affects GPA. For example, business school students usually work for a while before getting their MBA. If you think that students with higher GPAs should earn more money after they graduate, then presumably you also would expect that students who earn more money before going to business schools will get higher GPAs.

The best traditional studies show that GPA accounts for about 3% of job performance, as measured by income and performance reviews among other things. (IIRC Alfie Kohn cites this study in his book What Does It Mean To Be Well Educated?) It will be interesting to see whether or not running the study backwards yields similar results.